How can a specific connectivity pattern be stored in an optimally compact representation?
Solution

In learning systems, the output of learning is a set of parameters. These parameters can be a tensor in the case of a CNN, a representation of a directed graph in the case of recursive network designs, or any other structure holding the results of training.

The general case of compactly storing the result of training involves four process elements. These elements can be combined into one algorithm if needed.


Encoding of ordinals
Lossless conversion of IEEE floats
Serialization of the structure
Lossless compression of the stream


Upon retrieval, the elements are reversed.


Decompression of the stream
Parsing to reassemble structure
Expansion of IEEE float representations
Decoding of ordinals


The encoding of ordinals requires the mapping of values to the minimal number of bytes or, most optimally, bits. The mapping must be reversible, meaning that there can be no information loss, so that decoding is completely reliable.

If the encoding and serialization packs the information tightly, there may be little gain with a general compression algorithm such as LZ4.

Notions of General Intelligence

Before devoting much time on developing humanoid AGI and modeling cognition and states of mind, it may be useful to curb expectations away from trendy ideas. There is much conflict between the naive conceptions of general intelligence and the realities of neurological systems in animals and people, which are far more sophisticated than implied in the trendy media hype. The most important considerations are these.


The complexity of networks in the brain
That there is a significant varieties of neurons in brains
The impact of neuroplasticity
Complexity of chemical signaling independent from nerves
Whether intelligence is in fact multi-dimensional
Large number of genes that correlate with intelligence
The academic slant of concepts regarding intelligence
Difference between brain signal topology and computing models 
Data-centricity


There are many articles on the web on these topics, along with critiques of concepts such as the g-factor and the idea of general problem solving and general intelligence. There are several questions here on this topic.


Why did Artificial Intelligence projects fail?
Can the IQ of an AI program be measured?
Can a brain be intelligent without a body?
Is the singularity concept mathematically flawed?
Is there a ceiling to intelligence itself?
Self-conscious artifical intelligence
Is the Turing Test, or any of its variants, a reliable test of artificial intelligence?


There is no value in discouraging curiosity and serious research into understanding the nature of intelligence or efforts to expanding the boundaries of computing. The above comments are to assist in bringing the starting point of such inquiry into the realm of enthusiasm anchored by scientific methodology. Conjecture makes for great movie plots, but does not further science and does not lead to real world technology products and services.